Related papers: Subsonic time-periodic solution to compressible Eu…
In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term $\beta(t,x)\rho|u|^{\alpha}u$ in a bounded domain, which can be used to describe gas transmission in a nozzle.~The model is imposed a…
In this paper, one-dimensional nonisentropic compressible Euler equations with linear damping $\alpha(x)\rho u$ are analyzed.~We want to explore the conditions under which a subsonic temporal periodic boundary can trigger a time-periodic…
In this paper, we study one-dimensional nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions. With the aid of the energy methods, we prove the existence and uniqueness of the time-periodic supersonic…
In this paper, we study the initial-boundary value problem of one-dimensional isentropic compressible Euler equations with the source term $\beta\rho|u|^{\alpha}u$. By means of wave decomposition and the uniform a-priori estimates, we prove…
We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time…
In this article, time periodic problem of the compressible Euler equations with damping on the whole space is studied. It is well known that in the Euler system, long-time behavior of solutions is a more delicate problem due to lack of the…
In the field of differential equations, particularly fluid dynamics, many researchers have shown an interest in the behavior of time periodic solutions. In this paper, we study isentropic gas flow in a bounded interval and apply a time…
In this work we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow…
For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such…
This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad…
In this paper, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME)…
In this paper, the smooth solution of the physical vacuum problem for the one dimensional compressible Euler equations with time-dependent damping is considered. Near the vacuum boundary, the sound speed is $C^{1/2}$-H\"{o}lder continuous.…
In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…
In this note, we prove that the solutions obtained to the spherically symmetric Euler equations in the recent works [2, 3] are weak solutions of the multi-dimensional compressible Euler equations. This follows from new uniform estimates…
We develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic-hyperbolic composite-mixed type for subsonic flows. The method is applied…
We prove the existence of ``pure tone'' nonlinear sound waves of all frequencies. These are smooth, time periodic, oscillatory solutions of the $3\times3$ compressible Euler equations satisfying periodic or acoustic boundary conditions in…
In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to the compressible Euler equations with damping time-asymptotically converges to the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In…
The goal of this note is to show that, also in a bounded domain $\Omega \subset \mathbb{R}^n$, with $\partial \Omega\in C^2$, any weak solution, $(u(x,t),p(x,t))$, of the Euler equations of ideal incompressible fluid in $\Omega\times (0,T)…
We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…